Research On Parametric Resonance Of Supender System Of Suspension Bridge And Vibration Control By Using TMD

Parametric vibration of suspender system of a suspension bridge may be excited easily under wind load and vehicle load, which may damage the key parts to failure. It’s necessary to find the law of parametric resonance of suspender system of suspension bridges, and take suitable measure to control vibration effectively. On the basis of summarizing the mechanism and related theory of parametric resonance of cables aboard and at home, this article has established single suspender, beam-suspender and beam-suspender-main cable system models, then derive vibration Differential equation, analyze variable systems’ law of parametric vibration by using fourth order rugger kutta method, besides, analyzing vibration control to find parameter factor and effect of vibration control by using TMD. The main content is as below:1. Dynamic modal of single suspender system has been established, by time-history and sweeping frequency analysis, confirmed that primary resonance and parametric resonance will be excited when the external excitation frequency and the frequency of suspender ratio are1:1and12, and there are frequency band of each systems, in addition, parametric resonance frequency band is wider than primary resonance; research of effect on parametric resonance and primary resonance on length of suspender, initial tension, which shows that the longer the suspender, the more significant of the amplitude of parametric resonance and the initial tension can delay the excitation of primary resonance.2. Dynamic modal of beam-suspender system has been established, by time-history and sweeping frequency analysis, confirmed that primary resonance and parametric resonance will be excited when the external excitation frequency, frequency of beam and the frequency of suspender are1:1:1and22:1, analyzing how external excitation amplitude and frequency have effected primary resonance and parametric resonance. Using Den Hartog’s theory to design frequency ratio and damping ratio, and research on the robust performance when the parameter vary, to optimize the parameters of TMD. The article have Confirmed that TMD installed on beam can effectively control the parametric resonance.3. Dynamic modal of beam-suspender-main cable system of free vibration has been established, multiple time scales method analyzing have been done after decoupling dynamic equation,which derives possible resonance frequency ratio of the system. Rugger-kutta method is used to calculate the relationship of non-decoupling frequency, there are four resonance systems. Sweeping frequency analysis of the four resonance systems indicate the potential resonance frequency. Optimal TMD that is assigned with the Den Hartog theory is used to control the vibration of two of four systems prove that TMD can effectively control primary resonance and reduce the resonance band of parametric resonance.